Building up an old Avalance LE frame.....need some help with parts sizing...

Hello,
I've had this older Avalanche LE frame for awhile. It's smoke in color with yellow decals.
I want to build this up for my sister.
What is the seatpost size that I'll need?
Also, what's the bottom bracket size?

The easiest way to figure that out is to measure it.
If you can take it to a bike shop they will have calipers to measure the seat tube diameter and the BB shell width.
If you have a tape measure or ruler with mm markings you could measure it yourself. The seatpost diameter might be hard to do that way, but you could get the BB shell for sure.